November Lectures

Week of November 3-7

Nov 4: Introduction to multivariate generating functions. Parameters. Their usage in computing expected values, variances and other moments. [Deadline minor project.] [A2 in; A3 out]
Nov 6: Example of binomial distribution. Labelled constructions and exponential generating functions.

Week of November 10-14

Nov 11: The admissibility theorem for labelled constructions. Permutations: basic countings, involutions. Expectation and variance of the number of cyles in a random permutation. Comments about Assignment 3.
Nov 13: Generalization to the number of components in admissible constructions. Complex asymptotics: the connection between generating functions and complex asymptotics.

Week of November 17-21

Nov 18: Complex asymptotics: analytic functions, singularities, radius of convergence, dominant singularity, etc.
Nov 20: The exponential growth formula and examples. Meromorphic functions and residues: Cauchy's residue theorem, and Cauchy's coefficient formula. Asymptotics of rational functions and examples.

Week of November 24-28

Nov 25: Comments about assignment 3. Asymptotics of meromorphic functions and examples. Introduction to singularity analysis.
Nov 27: Singularity analysis: brief comments on the Gamma function, Hankel contours, and transfer lemmas; examples of its usage.

December

Dec 4: [A3 in]
December 12: deadline major project.
December 18: oral presentations.

To October lectures.